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Piecewise semialgebraic sets
  • 时间：0
  • 分类：O15[理学—数学;理学—基础数学]
  • 作者机构：Dalian Univ Technol, Inst Math Sci, Dalian 116024, Peoples R China
  • 相关基金：Supported by the National Natural Science Foundation of China （Grant Nos. 10271022 and 60373093）.
  • 相关项目：计算机辅助几何设计的一些新方法及其应用
作者： C.G. Zhu, R.H. Wang
关键词： 半代数集, 代数几何, Tarski-Seidenberg法则, 分段性, 实系数, Algebraic geometry, Semialgebraic geometry, Tarski-Seidenberg Principle, Multivariate splines, Piecewise semialgebraic sets
中文摘要：

Semialgebraic 集合是真正是真实代数学的几何学的一个特殊特征的目标。这篇论文论述片明智的半代数学设置布尔联合，它是 R~nsatisfying 的子集多有真实系数的变量花键方程和不平等。而且，在设计下面的稳定性和 C~ μ piece-wisesemialgebraic 集合的尺寸也被讨论。

英文摘要：

Semialgebraic sets are objects which are truly a special feature of real algebraic geometry. This paper presents the piecewise semialgebraic set, which is the subset of Rn satisfying a boolean combination of multivariate spline equations and inequalities with real coefficients. Moreover, the stability under projection and the dimension of C^μ piecewise semialgebraic sets are also discussed.

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